Problem: What is the next term of the geometric sequence? $20,-10,5,$
Explanation: In a geometric sequence there's a constant ratio between subsequent terms. Let's find that ratio, and use it to find which term should come after the last one that is given, which is $5$. Each term is ${-\dfrac12}$ times the term before it. ${\times \left(-\dfrac12\right)\,\curvearrowright}$ ${\times \left(-\dfrac12\right)\,\curvearrowright}$ $20,$ $-10,$ $5$ So the next term is $5\cdot\left({-\dfrac12}\right)=-\dfrac52$. The missing term is $-\dfrac52$.